Topics in Mathematics Münster

Research Interests

$\bullet$ Homotopy theory and Higher Algebra.
$\bullet$ Algebraic $K$-theory.
$\bullet$ Field theories and mathematical Physics.
$\bullet$ (topological) Hochschild homology and non-commutative geometry.

Selected Publications of Prof. Dr. Thomas Nikolaus

$\bullet$ T. Nikolaus and S. Sagave. Presentably symmetric monoidal $\infty$-categories are represented by symmetric monoidal model categories. Algebr. Geom. Topol., 17(5):3189–3212, 2017.

$\bullet$ D. Gepner, R. Haugseng, and T. Nikolaus. Lax colimits and free fibrations in $\infty$-categories. Doc. Math., 22:1225–1266, 2017.

$\bullet$ U. Bunke, T. Nikolaus, and M. Völkl. Differential cohomology theories as sheaves of spectra. J. Homotopy Relat. Struct., 11(1):1–66, 2016.

$\bullet$ D. Gepner, M. Groth, and T. Nikolaus. Universality of multiplicative infinite loop space machines. Algebr. Geom. Topol., 15(6):3107–3153, 2015.

$\bullet$ U. Bunke and T. Nikolaus. $T$-duality via gerby geometry and reductions. Rev. Math. Phys., 27(5):1550013, 46 pp., 2015.

$\bullet$ T. Nikolaus. Algebraic K-theory of $\infty$-operads. J. K-Theory, 14(3):614–641, 2014.

$\bullet$ T. Nikolaus and K. Waldorf. Lifting problems and transgression for non-abelian gerbes. Adv. Math., 242:50–79, 2013.

$\bullet$ T. Nikolaus, C. Sachse, and C. Wockel. A smooth model for the string group. Int. Math. Res. Not. IMRN, (16):3678–3721, 2013.

$\bullet$ T. Nikolaus and C. Schweigert. Equivariance in higher geometry. Adv. Math., 226(4):3367–3408, 2011.

$\bullet$ T. Nikolaus. Algebraic models for higher categories. Indag. Math. (N.S.), 21(1-2):52–75, 2011.

Current Cluster Publications of Prof. Dr. Thomas Nikolaus

$\bullet $ Yonatan Harpaz, Thomas Nikolaus, and Victor Saunier. Trace methods for stable categories I: The linear approximation of algebraic K-theory. arXiv e-prints, November 2024. arXiv:2411.04743.

$\bullet $ Thomas Nikolaus and Maria Yakerson. An alternative to spherical Witt vectors. arXiv e-prints, May 2024. arXiv:2405.09606.

$\bullet $ Benjamin Antieau, Achim Krause, and Thomas Nikolaus. On the $K$-theory of $\bf Z$$/p^n$. arXiv e-prints, May 2024. arXiv:2405.04329.

$\bullet $ Shachar Carmeli, Thomas Nikolaus, and Allen Yuan. Maps between spherical group rings. arXiv e-prints, May 2024. arXiv:2405.06448.

$\bullet $ Emanuele Dotto, Achim Krause, Thomas Nikolaus, and Irakli Patchkoria. Witt vectors with coefficients and TR. arXiv e-prints, December 2023. arXiv:2312.12971.

$\bullet $ Baptiste Calmès, Emanuele Dotto, Yonatan Harpaz, Fabian Hebestreit, Markus Land, Kristian Moi, Denis Nardin, Thomas Nikolaus, and Wolfgang Steimle. Hermitian $K$-theory for stable ∞-categories I: Foundations. Selecta Mathematica. New Series, 29(1):Paper No. 10, 269, November 2023. doi:10.1007/s00029-022-00758-2.

$\bullet $ Markus Land, Thomas Nikolaus, and Marco Schlichting. L-theory of $C^*$-algebras. Proceedings of the London Mathematical Society, 127(5):1451–1506, October 2023. doi:10.1112/plms.12564.

$\bullet $ Benjamin Antieau, Achim Krause, and Thomas Nikolaus. Prismatic cohomology relative to δ-rings. arXiv e-prints, October 2023. arXiv:2310.12770.

$\bullet $ Achim Krause, Jonas McCandless, and Thomas Nikolaus. Polygonic spectra and TR with coefficients. arXiv e-prints, February 2023. arXiv:2302.07686.

$\bullet $ Benjamin Antieau, Akhil Mathew, Matthew Morrow, and Thomas Nikolaus. On the Beilinson fiber square. Duke Math. J., 171(18):3707–3806, December 2022. doi:10.1215/00127094-2022-0037.

$\bullet $ Achim Krause and Thomas Nikolaus. Bökstedt periodicity and quotients of DVRs. Compos. Math., 158(8):1683–1712, September 2022. doi:10.1112/s0010437x22007655.

$\bullet $ Benjamin Antieau, Achim Krause, and Thomas Nikolaus. On the K-theory of $\mathbb Z/p^n$ – announcement. arXiv e-prints, April 2022. arXiv:2204.03420.

$\bullet $ Emanuele Dotto, Achim Krause, Thomas Nikolaus, and Irakli Patchkoria. Witt vectors with coefficients and characteristic polynomials over non-commutative rings. Compos. Math., 158(2):366–408, February 2022. doi:10.1112/S0010437X22007254.

$\bullet $ Fabian Hebestreit, Markus Land, and Thomas Nikolaus. On the homotopy type of L-spectra of the integers. J. Topol., 14(1):183–214, March 2021. doi:10.1112/topo.12180.

$\bullet $ Clark Barwick, Saul Glasman, Akhil Mathew, and Thomas Nikolaus. K-theory and polynomial functors. arXiv e-prints, February 2021. arXiv:2102.00936.

$\bullet $ Benjamin Antieau and Thomas Nikolaus. Cartier modules and cyclotomic spectra. J. Amer. Math. Soc., 34(1):1–78, January 2021. doi:10.1090/jams/951.

$\bullet $ Baptiste Calmès, Emanuele Dotto, Yonatan Harpaz, Fabian Hebestreit, Markus Land, Kristian Moi, Denis Nardin, Thomas Nikolaus, and Wolfgang Steimle. Hermitian K-theory for stable ∞-categories III: Grothendieck-Witt groups of rings. arXiv e-prints, September 2020. arXiv:2009.07225.

$\bullet $ Baptiste Calmès, Emanuele Dotto, Yonatan Harpaz, Fabian Hebestreit, Markus Land, Kristian Moi, Denis Nardin, Thomas Nikolaus, and Wolfgang Steimle. Hermitian K-theory for stable ∞-categories II: Cobordism categories and additivity. arXiv e-prints, September 2020. arXiv:2009.07224.

$\bullet $ Lars Hesselholt and Thomas Nikolaus. Algebraic $K$-theory of planar cuspidal curves. In $K$-theory in algebra, analysis and topology, volume 749 of Contemp. Math., pages 139–148. Amer. Math. Soc., [Providence], RI, March 2020. doi:10.1090/conm/749/15070.

$\bullet $ Thomas Nikolaus and Konrad Waldorf. Higher geometry for non-geometric T-duals. Commun. Math. Phys., 374(1):317–366, February 2020. doi:10.1007/s00220-019-03496-3.

$\bullet $ Lars Hesselholt and Thomas Nikolaus. Topological cyclic homology. In Handbook of homotopy theory, CRC Press/Chapman Hall Handb. Math. Ser., pages 619–656. January 2020. doi:10.1201/9781351251624-15.

$\bullet $ Ulrich Bunke and Thomas Nikolaus. Twisted differential cohomology. Algebr. Geom. Topol., 19(4):1631–1710, August 2019. doi:10.2140/agt.2019.19.1631.

$\bullet $ Achim Krause and Thomas Nikolaus. Bökstedt periodicity and quotients of DVRs. arXiv e-prints, July 2019. arXiv:1907.03477.

$\bullet $ Tobias Barthel, Markus Hausmann, Niko Naumann, Thomas Nikolaus, Justin Noel, and Nathaniel Stapleton. The Balmer spectrum of the equivariant homotopy category of a finite abelian group. Invent. Math., 216(1):215–240, April 2019. doi:10.1007/s00222-018-0846-5.

$\bullet $ Thomas Nikolaus and Peter Scholze. Correction to “On topological cyclic homology”. Acta Math., 222(1):215–218, March 2019. doi:10.4310/ACTA.2019.v222.n1.a2.

$\bullet $ Markus Land and Thomas Nikolaus. On the relation between $K$- and $L$-theory of $C^*$-algebras. Math. Ann., 371(1-2):517–563, November 2018. doi:10.1007/s00208-017-1617-0.

$\bullet $ Benjamin Antieau, Akhil Mathew, and Thomas Nikolaus. On the Blumberg-Mandell Künneth theorem for TP. Selecta Math. (N.S.), 24(5):4555–4576, August 2018. doi:10.1007/s00029-018-0427-x.

$\bullet $ Ulrich Bunke, Thomas Nikolaus, and Georg Tamme. The Beilinson regulator is a map of ring spectra. Adv. Math., 333:41–86, July 2018. doi:10.1016/j.aim.2018.05.027.

$\bullet $ Thomas Nikolaus and Peter Scholze. On topological cyclic homology. Acta Math., 221(2):203–409, 2018. doi:10.4310/ACTA.2018.v221.n2.a1.